2026-09-23T15:58:58Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/44335 2023-07-11 col_2142_5131 col_2142_8859 com_2142_5130 com_2142_8858 com_2142_234

Stone, Michael Ryu, Shinsei Stone, Michael Chiang, Tai-Chang Gilbert, Matthew J. Cooper, S. Lance Chiu, Ching-Kai 2013-05-24T22:08:12Z 2013-05-24T22:08:12Z 2013-05 2013-05-24T22:08:12Z 2013-05 We study a topological classification of insulators and superconductors in the presence of non-spatial discrete symmetries in the Altland-Zirnbauer classification and spatial symmetries in any spatial dimension. We provide a unified method, the construction of bulk Dirac Hamiltonians in minimal matrix dimension, to classify topological phases. Using this method, we first reproduce the classification of non-spatial symmetric topological insulators and superconductors in the Altland-Zirnbauer symmetry classes. Such non-trivial topological insulators and superconductors possess protected gapless modes in each boundary. Furthermore, we extend the classification to spatial symmetric systems, such as reflection symmetry. When a specific boundary that does not break system's symmetries is introduced in these non-trivial topological systems, gapless modes are present at this boundary. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-04-15T21:14:02Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 2 bundle_Chiu_Ching-Kai.zip: 1365703 bytes, checksum: 7f5882de50e0567fb484fc129c05b867 (MD5) Chiu_Ching-Kai.pdf: 2203132 bytes, checksum: 53d512b68edf11ce81a650c58d5e2902 (MD5) Made available in DSpace on 2013-05-24T22:08:12Z (GMT). No. of bitstreams: 3 Ching-Kai_Chiu.pdf: 2203132 bytes, checksum: 53d512b68edf11ce81a650c58d5e2902 (MD5) bundle_Chiu_Ching-Kai.zip: 1365703 bytes, checksum: 7f5882de50e0567fb484fc129c05b867 (MD5) license.txt: 4061 bytes, checksum: 335af38e3e06321f5875b5308f575ce3 (MD5) http://hdl.handle.net/2142/44335 en Copyright 2013 Ching-Kai Chiu classification topological insulators topological superconductors topological crystalline insulators The classification of topological insulators and superconductors for non-spatial and spatial symmetries text Physics 1244 Physics 0240 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Physics -UIUC 10KS0240PHD